By using a one-zone chemical and spectrophotometric evolution model of a disk galaxy undergoing a dusty starburst, we investigate numerically the optical spectroscopic properties in order to explore galaxy evolution in distant clusters. We adopt an assumption that the degree of dust extinction (represented by AV) depends on the ages of starburst populations in such a way that younger stars have larger AV (originally referred to as selective dust extinction by Poggianti & Wu). In particular, we investigate how the time evolution of the equivalent widths of [O II] λ3727 and Hδ are controlled by the adopted age dependence. This leads to the following three main results: (1) If a young stellar population (with an age of ~106 yr) is more heavily obscured by dust than an old one (>108 yr), the galaxy can show an "e(a)" spectrum characterized by strong Hδ absorption and relatively modest [O II] emission. (2) A dusty starburst galaxy with an e(a) spectrum can evolve into a poststarburst galaxy with an a + k (or k + a) spectrum 0.2 Gyr after the starburst and then into a passive one with a k-type spectrum 1 Gyr after the starburst. This result clearly demonstrates an evolutionary link between galaxies with different spectral classes [i.e., e(b), e(a), a + k, k + a, and k]. (3) A dusty starburst galaxy can show an a + k or k + a spectrum even in the dusty starburst phase if the age-dependence of dust extinction is rather weak; i.e., if young starburst populations with different ages (≤107 yr) are uniformly obscured by dust.